Question: Simplify. Remove all perfect squares from inside the square root. Assume $x$ is positive. $\sqrt{54x^7}=$
Solution: Factor $54$ and find the greatest perfect square: $54=3\cdot 3\cdot 3\cdot 2=3^2\cdot 6$ Find the greatest perfect square in $x^7$ : $x^7=\left(x^3\right)^2\cdot x$ $\begin{aligned} \sqrt{54x^7}&=\sqrt{3^2\cdot 6\cdot\left(x^3\right)^2\cdot x} \\\\ &=\sqrt{3^2}\cdot \sqrt6 \cdot\sqrt{\left(x^3\right)^2}\cdot \sqrt x \\\\ &=3\cdot\sqrt6\cdot x^3\cdot\sqrt x \\\\ &=3x^3\sqrt{6x} \end{aligned}$